In recent years evidence has been accumulating that personalities are not only found in humans1 but also in a wide range of other animal species2, 3, 4, 5, 6, 7, 8. Individuals differ consistently in their behavioural tendencies and the behaviour in one context is correlated with the behaviour in multiple other contexts. From an adaptive perspective, the evolution of animal personalities is still a mystery, because a more flexible structure of behaviour should provide a selective advantage9, 10, 11. Accordingly, many researchers view personalities as resulting from constraints imposed by the architecture of behaviour7 (but see ref. 12). In contrast, we show here that animal personalities can be given an adaptive explanation. Our argument is based on the insight that the trade-off between current and future reproduction13 often results in polymorphic populations14 in which some individuals put more emphasis on future fitness returns than others. Life-history theory predicts that such differences in fitness expectations should result in systematic differences in risk-taking behaviour15. Individuals with high future expectations (who have much to lose) should be more risk-averse than individuals with low expectations. This applies to all kinds of risky situations, so individuals should consistently differ in their behaviour. By means of an evolutionary model we demonstrate that this basic principle results in the evolution of animal personalities. It simultaneously explains the coexistence of behavioural types, the consistency of behaviour through time and the structure of behavioural correlations across contexts. Moreover, it explains the common finding that explorative behaviour and risk-related traits like boldness and aggressiveness are common characteristics of animal personalities2, 3, 4, 5, 6, 7, 8.